DeepAI AI Chat
Log In Sign Up

Communication-Channel Optimized Partition

01/06/2020
by   Thuan Nguyen, et al.
Oregon State University
0

Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the posterior probability p(X|Y). This result finally provides a polynomial-time algorithm to find the globally optimal quantizer.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/31/2019

Minimizing Impurity Partition Under Constraints

Set partitioning is a key component of many algorithms in machine learni...
01/07/2020

Single-bit Quantization Capacity of Binary-input Continuous-output Channels

We consider a channel with discrete binary input X that is corrupted by ...
11/09/2018

An output-sensitive polynomial Time Algorithm to partition a Sequence of Integers into Subsets with equal Sums

The well-known PARTITION problem: Given positive integers n, k and t suc...
02/25/2020

Well-partitioned chordal graphs: obstruction set and disjoint paths

We introduce a new subclass of chordal graphs that generalizes split gra...
07/13/2018

Approximation Algorithms for Clustering via Weighted Impurity Measures

An impurity measures I:R^k →R^+ maps a k-dimensional vector v to a non-...
06/13/2017

Lost Relatives of the Gumbel Trick

The Gumbel trick is a method to sample from a discrete probability distr...